Comptes Rendus
Geometry
Abelian fibrations and SYZ mirror conjecture
Comptes Rendus. Mathématique, Volume 350 (2012) no. 13-14, pp. 689-692.

SYZ mirror conjecture predicts that a Calabi–Yau manifold X consists of a family of tori which are dual to a family of special Lagrangian tori on the mirror dual manifold Xˆ. Here we consider a fibration of polarized abelian varieties and we construct a dual one. Moreover we prove that they are equivalent at the level of derived categories.

La conjecture de « symétrie miroir SYZ » prédit quʼune variété de Calabi–Yau X consiste en une famille de tores qui sont duaux dʼune famille de tores lagrangiennes spéciaux dans la variété miroir duale Xˆ. Nous considérons ici une fibration de variétés abéliennes polarisées et nous en construisons la duale. De plus, nous montrons quʼelles sont équivalentes au niveau des catégories dérivées.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2012.07.011

Cristina Martínez 1, 2

1 Universitat, Departament de Matematiques, Edifici C, Facultad de Ciencies, 08193 Bellaterra, Barcelona, Spain
2 Dipartimento di Matematica “Guido Castelnuovo”, Sapienza Università di Roma, P.le Aldo Moro, 5, 00185 Roma, Italy
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Cristina Martínez. Abelian fibrations and SYZ mirror conjecture. Comptes Rendus. Mathématique, Volume 350 (2012) no. 13-14, pp. 689-692. doi : 10.1016/j.crma.2012.07.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.07.011/

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[2] R. Dijkgraaf Mirror symmetry and elliptic curves, Texel Island, 1994 (Progr. Math.), Volume vol. 129, Birkhäuser, Boston, MA (1995), pp. 149-163

[3] R. Donagi; T. Pantev Torus fibrations, gerbes, and duality (in Memoirs of the AMS) | arXiv

[4] D. Henández Ruipérez; A.C. López Martín; F. Sancho de Salas Relative integral functors for singular fibrations and singular partners, J. Eur. Math. Soc. (JEMS), Volume 11 (2009), pp. 597-625

[5] C. Martínez; A.N. Todorov Derived equivalences of Calabi–Yau fibrations | arXiv

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